用p'表示非p，用乘表示合取，用加表示析取。[（p+q）→r]→p=[(p+q)'+r]'+p=(p+q)r'+p=pr'+qr'+p=p+qr'=(p+q)(p+r')。命题公式(propositional formula)亦称合式公式，是数理逻辑术语，它是按照一定规律形成的符号序列，在命题演算中，公式通常用归纳定义给出，例如，在一个具有...
(3)E=∑n=0∞λnEn based on the Taylor formula En=1n!dnEdλn and evaluate derivatives of the secular determinant with respect to λ (implying a spectral method for the solution of the Schrödinger equation). While λ introduced in Eq. (1) is often considered an auxiliary tool that even...
We given an explicit p-adic expansion of ∑_(j=1)~(*np)q~j/[j]~r as a power series in n which generalizes the formula of Andrews (Discrete Math. 204 (1999) 15). Indeed, this is a q-analogue result due to Washington (J. Number Theory 69 (1998) 50), corresponding to the cas...
当x=\pi^2\lambda_n^2/(6k^2) 时r^2=2\pi^2\lambda_n^2/3=B^2\lambda_n^2/k^2 ,所以有: \begin{aligned} Q_k(n) &=k^32^{-\frac32}\pi^{-\frac32}\lambda_n^{-3}\cdot{B^2\lambda_n^2\over2\pi^\frac12k^2}{\mathrm d\over\mathrm d(B\lambda_n/k)}\left(\cosh(...
(i) If g ∈C <sub class="a-plus-plus">ϱ</sub> (Hölder-Zygmund spaces), then f → gf is a bounded operator from A into A, provided that ϱ=ϱ(s, p, q, n) is large enough. (ii) There are given sufficient conditions for s, p, and q ensuring that A is a sub...
Question: What is the truth table for the below formula? {eq}\sim (p \to q) {/eq} Truth Table: In order to create the truth table of a given symbolic statement, we need to know first the set of rules in logic especially the hierarchy of connectives as well as the rules i...
for n\ge 2, with initial conditions Q_{0}(x)=1 and Q_{1}(x)=-2x+1. Proof of Proposition 2.11 By differentiating the explicit formula (2.3), we obtain \begin{aligned} Q_{k+n}^{(k)}(x) =\sum _{i=0}^{n}(-1)^{i+k}\frac{(i+k)!}{i!}\left( {\begin{array}{c}...
Factors of binomial sums from the Catalan triangle By using the Newton interpolation formula, we generalize the recent identities on the Catalan triangle obtained by Miana and Romero as well as those of Che... GJ Zeng - 《Journal of Number Theory》...
现在令 x=\pi^2\lambda_n^2/6 则有r=B\lambda_n 其中B=\pi\sqrt{2/3} 。这表明: \begin{aligned} 2\pi Q(n) &={B^2\over2^{\frac32}\pi\lambda_n}{\mathrm d\over\mathrm d(B\lambda_n)}\left(\cosh(B\lambda_n)\over B\lambda_n\right) \\ &={1\over2^{\frac32}\pi\lam...
Three solutions for a class of quasilinear elliptic systems involving the [formula omitted]-Laplacian The existence of at least three weak solutions is established for a class of quasilinear elliptic systems involving the ( p , q )-Laplacian with Dirichlet ... C Li,CL Tang - 《Nonlinear ...